Spatial Decay Estimates And Continuous Dependence On Time Geometry In Generalized Thermoelasticity

This paper derives spatial decay bounds and continuous dependence on time geometry in a dynamical problem of linear anisotropic thermoelasticity. We proved that an energy expression is actually bounded above by a decaying exponential of a quadratic polynomial of the distance from the finite end of the cylinder. This is reminiscent of the decay rate in second order parabolic problem. We also investigate the question of continuous dependence on the initial time geometry for solutions of the standard initial boundary value problem. This is done by deriving appropriate a priori inequality which displays continuous dependence on the initial time geometry in the weak energy norm.